Henri & Renaud Lifchitz's PRP Top records

What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!

Submit your PRPs

See the Top discoverers
See the Latest PRPs
Search by form


1-250	251-500	501-750	751-1000	1001-1250	1251-1500	1501-1750	1751-2000
2001-2250	2251-2500	2501-2750	2751-3000	3001-3250	3251-3500	3501-3750	3751-4000
4001-4250	4251-4500	4501-4750	4751-5000	5001-5250	5251-5500	5501-5750	5751-6000
6001-6250	6251-6500	6501-6750	6751-7000	7001-7250	7251-7500	7501-7750	7751-8000
8001-8250	8251-8500	8501-8750	8751-9000	9001-9250	9251-9500	9501-9750	9751-10000

Rank	Probable prime	Digits (> 50000)	Who ?	When ?
9753	(2^311580+7)/591329	93790	Lelio R Paula	06/2013
9751	10^93790-123456789	93790	Robert Price	02/2020
9752	10^93790-157517	93790	Patrick De Geest	04/2020
9754	(49*10^93782+293)/9	93783	Robert Price	03/2021
9755	12^86900-77	93781	Lelio R Paula	06/2016
9756	2^311508-109769	93774	Enzo Doria	04/2014
9757	2^311486-1859621	93767	Enzo Doria	03/2016
9758	Phi(93811,10)/968129521/2109997013/3280113810431/639637782545831	93765	Kurt Beschorner	04/2015
9759	(10^93811-1)/(996812952121099970133280113810431639637782545831)	93765	Gord Palameta	10/2018
9760	2^311471+311469	93763	Renaud Lifchitz	01/2003
9761	(88*10^93760-1)/3	93762	Robert Price	10/2017
9762	2^311426+79459	93749	Enzo Doria	06/2016
9763	21537^21634+21634^21537	93745	Norbert Schneider	04/2020
9764	2^311409+111546435	93744	Paul Bourdelais	10/2021
9765	(2^311360+3078)/2	93729	Stefano Morozzi	09/2020
9766	(2^311341+2186)/2	93723	Stefano Morozzi	09/2020
9767	(2^311313+774)/2	93715	Stefano Morozzi	09/2020
9769	2^311294+5775	93709	Lelio R Paula	03/2016
9768	25155^5312+5312^25155	93709	Hans Havermann	09/2020
9770	2^311252-1017	93697	Lelio R Paula	03/2016
9771	2^311247-112041	93695	Enzo Doria	06/2014
9772	7*10^93692-83	93693	Robert Price	09/2017
9773	2^311205-109645	93683	Enzo Doria	04/2014
9774	5^134027-84	93681	Lelio R Paula	04/2016
9775	(2^311148-1017)/557	93663	Lelio R Paula	06/2013
9776	(2^311027-2^155514+1)/5	93628		11/2006
9777	26748^3161+3161^26748	93614	Hans Havermann	08/2020
9778	3^196192-28	93608	Robert Price	12/2013
9779	216091#+261433	93606	Makoto Morimoto	12/2015
9780	5^133917+68	93604	Lelio R Paula	04/2016
9781	2^310924-1709	93598	Yves Minet	03/2013
9782	24555^6476+6476^24555	93587	Hans Havermann	08/2020
9783	(2^310867+734)/2	93580	Stefano Morozzi	09/2020
9784	(266*10^93577-11)/3	93579	Robert Price	09/2016
9785	(16*10^93577+161)/3	93578	Robert Price	05/2016
9786	3^196113-56	93570	Lelio R Paula	04/2016
9787	2^310806-110345	93562	Enzo Doria	05/2014
9788	3^196093+86	93561	Lelio R Paula	04/2016
9789	2^310780-2327	93555	Yves Minet	10/2013
9790	30^63332+41	93550	Lelio R Paula	08/2012
9791	(21181*2^310707+1)/21	93536	Lelio R Paula	06/2014
9792	8*5^133807+7	93528	Lelio R Paula	10/2014
9793	2^310686+8193	93526	Lelio R Paula	03/2016
9794	22681^13282+13282^22681	93520	Hans Havermann	09/2020
9795	2^310646+63	93514	Lelio R Paula	11/2012
9796	(77*10^93508+31)/9	93509	Robert Price	10/2015
9797	((2^103536+1)^3-2)/3	93502	Serge Batalov	03/2023
9798	(1000907^15583+1)/1000908	93499	Faysal YAtim	04/2009
9799	(2*10^93497+7)/9	93497	Erik Branger	03/2011
9800	3^195958-112852	93496	Enzo Doria	07/2014
9801	2^310583+16385	93495	Lelio R Paula	03/2016
9802	(9913*2^310557-1)/35	93490	Lelio R Paula	04/2015
9803	9*7^110614+2	93481	Lelio R Paula	11/2014
9804	5*3^195914-2^195914	93476	Jon Grantham	08/2023
9805	(19*10^93467+83)/3	93468	Robert Price	08/2020
9806	2^310469-8295	93461	Lelio R Paula	03/2016
9807	2^310459-1159	93458	Yves Minet	11/2012
9808	6^120075-95	93437	Lelio R Paula	05/2016
9809	(2^310362+1758)/2	93428	Stefano Morozzi	09/2020
9810	256*19^73047+9	93412	Eric Chen	12/2022
9811	148^43041-147	93411	Norbert Schneider	05/2019
9813	2^310289+98327	93407	Yves Minet	11/2010
9812	fibonacci(446949)+3	93407	Jon Grantham	08/2023
9814	21769^19510+19510^21769	93395	Hans Havermann	08/2020
9815	2^310217-113143	93385	Enzo Doria	07/2014
9816	7^110494-68	93379	Lelio R Paula	04/2016
9817	2^310184-113093	93375	Enzo Doria	07/2014
9818	2^310180-110417	93374	Enzo Doria	05/2014
9819	gcd(V(1124905),5F(224981)(F(224981)-1)+1)	93372	Serge Batalov	04/2015
9820	(2^310173+3150)/2	93372	Stefano Morozzi	09/2020
9821	3^195669+68	93358	Lelio R Paula	04/2016
9822	10^93356+91	93357	Robert Price	04/2011
9823	10^93356-28313	93356	Patrick De Geest	08/2013
9824	(85*10^93346+23)/9	93347	Robert Price	11/2015
9825	(3^195648-5)/3158276	93342	Lelio R Paula	04/2013
9826	10^93333+191061	93334	Patrick De Geest	09/2022
9828	10^93333-4000001	93333	Robert Price	07/2021
9827	10^93333-44807	93333	Patrick De Geest	09/2022
9829	2^310006+213499	93322	Enzo Doria	09/2023
9830	3^195556+8680	93304	Lelio R Paula	04/2016
9831	2^309942-109991	93302	Enzo Doria	04/2014
9832	2^309926-1867301	93298	Enzo Doria	03/2016
9833	2^309924+85951	93297	Yves Minet	03/2011
9834	2^309896-4229	93288	Yves Minet	08/2018
9835	(86*10^93263-77)/9	93264	Robert Price	05/2016
9836	6^119836-125	93251	Lelio R Paula	05/2016
9837	(77*10^93249-257)/9	93250	Robert Price	10/2017
9838	21822^18749+18749^21822	93245	Hans Havermann	09/2020
9839	3^195430-2	93244	Theodore Burton	02/2007
9840	(13*10^93236+47)/3	93237	Robert Price	01/2017
9841	(67*10^93226-7)/3	93228	Robert Price	10/2017
9842	(86*10^93217-221)/9	93218	Robert Price	06/2017
9843	2^309637-16329	93211	Enzo Doria	04/2013
9844	(41*10^93207+49)/9	93208	Robert Price	04/2016
9845	2^309598+21529	93199	Enzo Doria	08/2023
9846	14^81312-57	93194	Lelio R Paula	06/2016
9847	41^57783-40	93192	Theodore Burton	02/2007
9848	3*10^93179-97	93180	Robert Price	08/2017
9849	5*7^110252-4	93175	Lelio R Paula	11/2014
9850	22022^16959+16959^22022	93140	Hans Havermann	08/2020
9851	83061!4-512	93137	Robert Price	11/2019
9852	25169^5016+5016^25169	93135	Hans Havermann	08/2020
9853	(483641^16384+1)/2	93135	Richard Fischer	02/2021
9854	2^309380-27	93133	Lelio R Paula	11/2012
9855	25653^4268+4268^25653	93127	Hans Havermann	08/2020
9856	(2^309355+1826)/2	93125	Stefano Morozzi	02/2021
9857	(2^309334+2710)/2	93119	Stefano Morozzi	09/2020
9858	23*10^93116-7	93118	Robert Price	03/2016
9859	(2^309270+3214)/2	93100	Stefano Morozzi	09/2020
9860	(29*10^93082+1)/3	93083	Robert Price	11/2015
9861	(2^309198+3738)/2	93078	Stefano Morozzi	09/2020
9862	(58*10^93062-13)/9	93063	Robert Price	09/2015
9863	(2^309138+1794)/2	93060	Stefano Morozzi	01/2021
9864	2^309131+1869383	93058	Enzo Doria	05/2016
9865	(2^309114+3610)/2	93053	Stefano Morozzi	09/2020
9866	2^309066-93	93039	Lelio R Paula	11/2012
9867	2^309063-113269	93038	Enzo Doria	07/2014
9868	3^194965+16	93022	Robert Price	10/2013
9869	(89*10^93019-737)/9	93020	Robert Price	01/2022
9870	2^308979+1869143	93012	Enzo Doria	05/2016
9871	5^133064+54	93008	Lelio R Paula	04/2016
9872	(2^308947+2750)/2	93003	Stefano Morozzi	01/2021
9873	(2^308905-509203)/119	92988	Lelio R Paula	06/2013
9874	(94*10^92981-49)/99	92981	Ray Chandler	07/2011
9875	(2*10^92976-17)/3	92976	Robert Price	08/2014
9876	24783^5642+5642^24783	92972	Hans Havermann	08/2020
9877	(472489^16384+1)/2	92969	Richard Fischer	01/2021
9878	2^308809+37967	92961	Phil Moore	03/2008
9879	(3^194825+5)/11656	92952	Lelio R Paula	04/2013
9880	14774^22291-22291^14774	92943	Norbert Schneider	08/2023
9881	norm(Mod(x,x^3-x-1)^760951-1)	92930	Paul Vanderveen	08/2022
9882	(2^308679+5)/1573	92919	Lelio R Paula	06/2013
9883	2^308650+513	92913	Lelio R Paula	02/2016
9884	5*7^109936+6	92908	Lelio R Paula	10/2014
9885	2*10^92897+89	92898	Robert Price	07/2016
9886	(19*23^68219-1867)/22	92896	Eric Chen	08/2023
9887	(2^308585+3182)/2	92894	Stefano Morozzi	09/2020
9888	(467307^16384+1)/2	92891	Richard Fischer	01/2021
9889	12^86073-29	92889	Lelio R Paula	06/2016
9890	2^308566-117	92888	Lelio R Paula	11/2012
9891	11594^22851-22851^11594	92872	Norbert Schneider	03/2022
9892	(17*10^92869-11)/3	92870	Robert Price	07/2015
9893	2^308459+75431	92856	Enzo Doria	04/2016
9894	2^308426-1866377	92846	Enzo Doria	03/2016
9895	24810^5521+5521^24810	92840	Hans Havermann	09/2020
9896	(96^46831-1)/95	92830	Paul Bourdelais	09/2017
9897	2^308349-112111	92823	Enzo Doria	06/2014
9898	9*10^92821+19	92822	Robert Price	05/2016
9899	2^308337-75	92819	Lelio R Paula	11/2012
9900	4*3^194508+7	92805	Lelio R Paula	08/2014
9901	22*25^66379-113	92796	Curtis Bright	05/2015
9902	24538^6047+6047^24538	92792	Hans Havermann	09/2020
9903	11^89101-1080	92790	Enzo Doria	12/2012
9904	2^308236-1867859	92789	Enzo Doria	04/2016
9905	12^85963+25	92770	Lelio R Paula	06/2016
9906	23692^8221+8221^23692	92753	Hans Havermann	08/2020
9907	7^109750-66	92750	Lelio R Paula	04/2016
9908	9*10^92742+11	92743	Robert Kinser	01/2017
9909	(2^308054+778)/2	92734	Stefano Morozzi	09/2020
9910	(21*2^308046-1)/8857	92729	Lelio R Paula	02/2014
9911	2^307997-110655	92717	Enzo Doria	05/2014
9912	L(443609)	92709	Renaud Lifchitz	11/2003
9913	10^92691+9	92692	Robert Price	03/2011
9914	10^92691-252291	92691	Patrick De Geest	08/2013
9915	(2^307883+3506)/2	92682	Stefano Morozzi	09/2020
9916	2^307879-2521	92681	Yves Minet	07/2014
9917	21269^21412+21412^21269	92666	Norbert Schneider	04/2020
9918	(2^307780-7)/19959669	92644	Lelio R Paula	06/2013
9919	14^80831+47	92643	Lelio R Paula	06/2016
9920	15^78744+92	92611	Lelio R Paula	07/2016
9921	65^51083-64	92610	Norbert Schneider	11/2014
9922	(2^307639+506)/2	92609	Stefano Morozzi	09/2020
9923	131^43737-130	92604	Norbert Schneider	02/2019
9924	6^118996-16943	92597	Enzo Doria	02/2013
9925	(16*10^92591+41)/3	92592	Robert Price	10/2017
9926	(2^307566+3094)/2	92587	Stefano Morozzi	09/2020
9927	(2^307528+1578)/2	92575	Stefano Morozzi	09/2020
9928	9*10^92573+83	92574	Robert Price	11/2020
9929	(3^194014-7)/2	92568	Lelio R Paula	04/2013
9930	(2^307498+570)/2	92566	Stefano Morozzi	09/2020
9931	(63^51439+1)/64	92555	Paul Bourdelais	08/2017
9932	(26*10^92546-77)/3	92547	Robert Price	02/2017
9933	3^193954+340	92540	Lelio R Paula	04/2016
9934	2^307407-307407^2	92539	Henri Lifchitz	05/2005
9935	24299^6430+6430^24299	92536	Hans Havermann	08/2020
9937	(17*10^92513-11)/3	92514	Robert Price	07/2015
9936	2^307322-399071	92514	Harrison Mesh	06/2022
9938	2^307318-4211	92512	Yves Minet	06/2011
9939	2^307280+193	92501	Lelio R Paula	11/2012
9940	20^71075-33	92471	Lelio R Paula	05/2016
9941	2^307126-78795	92455	Lelio R Paula	02/2016
9942	2^307125-49789	92454	Henri Lifchitz	08/2005
9943	fibonacci(442372)-2	92450	Jon Grantham	08/2023
9944	2^307099+23	92447	Lelio R Paula	11/2012
9945	129^43798+128	92440	Norbert Schneider	01/2019
9946	21826^17181+17181^21826	92435	Hans Havermann	09/2020
9947	Phi(277314,10)/3327769	92430	Makoto Kamada	05/2019
9948	(2^307022+1038)/2	92423	Stefano Morozzi	09/2020
9949	7*10^92414-69	92415	Robert Price	01/2017
9950	(9787*2^306975-1)/2129155	92407	Lelio R Paula	04/2015
9951	22280^14037+14037^22280	92402	Hans Havermann	09/2020
9952	2^306915+1873373	92391	Enzo Doria	06/2016
9953	2^306908+12915	92389	Lelio R Paula	02/2016
9954	21620^18759+18759^21620	92387	Hans Havermann	09/2020
9955	10^92386+111	92387	Jeppe Stig Nielsen	02/2023
9956	(2^306897+1142)/2	92385	Stefano Morozzi	09/2020
9957	19^72244-80	92383	Lelio R Paula	06/2016
9959	2^306849+75	92371	Lelio R Paula	11/2012
9958	(397*10^92369+53)/9	92371	Robert Price	11/2017
9960	2^306813-869688105	92360	Lelio R Paula	08/2016
9961	(2^306797+2694)/2	92355	Stefano Morozzi	09/2020
9962	21713^17914+17914^21713	92350	Hans Havermann	09/2020
9963	2^306672-109059	92318	Enzo Doria	04/2014
9964	(430463^16384+1)/2	92307	Richard Fischer	09/2020
9965	98*10^92295-9	92297	Robert Price	05/2023
9966	6^118604-17063	92292	Enzo Doria	02/2013
9967	21969^15878+15878^21969	92288	Hans Havermann	08/2020
9968	21690^17959+17959^21690	92276	Hans Havermann	08/2020
9969	(7613^23773-1)/7612	92273	Serge Batalov	08/2020
9970	(31*2^306487-1)/2291	92260	Lelio R Paula	02/2014
9971	2^306467-1835611	92256	Enzo Doria	04/2015
9972	2^306433+76427	92246	Enzo Doria	05/2016
9973	2^306430-113313	92245	Enzo Doria	07/2014
9974	(23*10^92244-59)/9	92245	Robert Price	03/2017
9975	(47*2^306398+1)/1384803	92231	Lelio R Paula	04/2015
9976	21436^20043+20043^21436	92217	Hans Havermann	09/2020
9977	(25*10^92186+59)/3	92187	Robert Price	05/2016
9978	2^306213-286183	92180	Enzo Doria	06/2015
9979	10^92178+61	92179	Robert Price	04/2011
9980	10^92178-175509	92178	Patrick De Geest	07/2013
9981	2^306200+1185	92176	Lelio R Paula	02/2016
9982	(2^306171+1514)/2	92167	Stefano Morozzi	09/2020
9983	2^306153+11	92162	Lelio R Paula	11/2012
9984	(2^306141-7)/5	92157	Lelio R Paula	06/2013
9985	21725^17454+17454^21725	92156	Hans Havermann	09/2020
9986	(26*10^92152-23)/3	92153	Robert Price	08/2016
9987	(2*10^92152+67)/3	92152	Robert Price	04/2017
9988	640*27^64370+17	92140	Eric Chen	02/2023
9989	21368^20457+20457^21368	92115	Hans Havermann	08/2020
9990	(2^305996+3018)/2	92114	Stefano Morozzi	09/2020
9991	410^92099+37^92099	92100	Mike Oakes	12/2010
9992	30504^1045+1045^30504	92096	Hans Havermann	08/2020
9993	24334^6085+6085^24334	92087	Hans Havermann	08/2020
9994	(2^305898+2262)/2	92085	Stefano Morozzi	01/2021
9995	(4591^25147-1)/4590	92083	Serge Batalov	08/2020
9996	115^44684+114	92081	Norbert Schneider	07/2018
9997	(416771^16384+1)/2	92077	Richard Fischer	08/2020
9998	(2^305867-2^152934+1)/5	92075		11/2006
9999	2^305851-109495	92071	Enzo Doria	04/2014
10000	(416213^16384+1)/2	92067	Richard Fischer	08/2020

Find by discoverer :

PRP Records

Probable Primes Top 10000

(293510 PRPs in the top)